0
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Let's define our line as $\lbrace (x,y) \in \mathbb{R}^2 \mid y=mx+b \rbrace$, then we need to find the probability that $q = mp+b$.

I don't know what else to do.

EDIT: For example what's the probability that a line passes through the origin? There are an infinite number of lines that passes through the origin but there are also an infinite number of lines that don't. So which is it?

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    $\begingroup$ What is the probability distribution involved? $\endgroup$ – user113102 May 14 '19 at 18:54
  • $\begingroup$ It’s probably zero. $\endgroup$ – amd May 14 '19 at 19:13
  • $\begingroup$ @user113102 If by that you mean the set of possible outcomes, then it's the sell of all possible pair of real numbers (\mathbb{R}^2) $\endgroup$ – user168651 May 14 '19 at 19:25
  • $\begingroup$ @amd Please check my edit $\endgroup$ – user168651 May 14 '19 at 19:30
  • $\begingroup$ The point is you need to specify how you're choosing the lines (or how you are choosing pairs of real numbers in $\mathbb{R}^2$). This is not a meaningful question without this information. $\endgroup$ – user113102 May 14 '19 at 19:34

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